Sum of three fractions is 21124On dividing the largest fraction

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Sum of three fractions is 2 11
24

On dividing the largest fraction by the smallest fraction 7/6 is obtained which is 1/3 greater than the middle fraction. The smallest fraction is

Let the three fractions be p, q and r, where p < q < r.
According to the question,

r	=	7	⇒ r =	7	p
p		6		6

Again, middle fraction

= q =	7	−	1	=	7 − 2	=	5
	6		3		6		6

∴ p + q + r = 2	11
	24

⇒ p +	5	+	7	p =	59
	6		6		24

⇒ p +	7p	=	59	−	5
	6		24		6

⇒	6p + 7p	=	59 − 20	=	39
	6		24		24

⇒ 13p =	39	×6 =	39
	24		4

⇒ p =	39	=	3
	4 × 13		4